document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246889>Question 246889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A standard deck of 52 playing cards consists of four different suits<BR>\n" );
document.write( "and 13 cards of different ranks in each suit. Four cards will be drawn at<BR>\n" );
document.write( "random without replacement from this deck. The probability that the<BR>\n" );
document.write( "four cards will be all the same suit is k times the probability that they<BR>\n" );
document.write( "will be all the same rank. What is the value of k? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180222 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=180222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I want P1(4 cards same suit), I don't care what<BR>\n" );
document.write( "the 1st card is, so I'll call P1(1st card) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "which means I'm certain to get any one of the cards.<BR>\n" );
document.write( "Now I have that card, and it is a certain suit, say<BR>\n" );
document.write( "clubs. There are 12 clubs left, so my chances of getting<BR>\n" );
document.write( "another club is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P2+=+12%2F51 ALIGN=MIDDLE  ALT=\"P2+=+12%2F51\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now  there are 11 clubs left <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P3+=+11%2F50 ALIGN=MIDDLE  ALT=\"P3+=+11%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P4+=+10%2F49 ALIGN=MIDDLE  ALT=\"P4+=+10%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bss%5D+=+P1%2AP2%2AP3%2AP4 ALIGN=MIDDLE  ALT=\"P%5Bss%5D+=+P1%2AP2%2AP3%2AP4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bss%5D+=+1%2A12%2F51%2A11%2F50%2A10%2F49 ALIGN=MIDDLE  ALT=\"P%5Bss%5D+=+1%2A12%2F51%2A11%2F50%2A10%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "There are 13 groups of 4 cards which are the same rank<BR>\n" );
document.write( "I don't care what the 1st card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P1+=+1 ALIGN=MIDDLE  ALT=\"P1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I've got the 1st card. Say it is a 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P2+=+3%2F51 ALIGN=MIDDLE  ALT=\"P2+=+3%2F51\"   DISABLED_style= \"max-width:90%; height:auto;\" > is P2(another 9)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P3+=+2%2F50 ALIGN=MIDDLE  ALT=\"P3+=+2%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > is P3(another 9)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P4+=+1%2F49 ALIGN=MIDDLE  ALT=\"P4+=+1%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" > is P4(another 9)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bsr%5D+=+1%2A3%2F51%2A2%2F50%2A1%2F49 ALIGN=MIDDLE  ALT=\"P%5Bsr%5D+=+1%2A3%2F51%2A2%2F50%2A1%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bss%5D+=+k%2AP%5Bsr%5D ALIGN=MIDDLE  ALT=\"P%5Bss%5D+=+k%2AP%5Bsr%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+P%5Bss%5D%2FP%5Bsr%5D ALIGN=MIDDLE  ALT=\"k+=+P%5Bss%5D%2FP%5Bsr%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%2812%2F51%2A11%2F50%2A10%2F49%29%2F%283%2F51%2A2%2F50%2A1%2F49%29 ALIGN=MIDDLE  ALT=\"k+=+%2812%2F51%2A11%2F50%2A10%2F49%29%2F%283%2F51%2A2%2F50%2A1%2F49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply right side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2851%2A50%2A49%29%2F%2851%2A50%2A49%29 ALIGN=MIDDLE  ALT=\"%2851%2A50%2A49%29%2F%2851%2A50%2A49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%2812%2A11%2A10%29%2F%283%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"k+=+%2812%2A11%2A10%29%2F%283%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+220 ALIGN=MIDDLE  ALT=\"k+=+220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );